BSSRDF: Bidirectional Surface Scattering ReflectanceDistribution Functions

Jared M. Dunne

C95 Adv. Graphics

Feb. 7, 2002

Based on:

"A Practical Model for Subsurface Light Transport"

Henrik Wann Jensen, Steve Marschner, Marc Levoy and Pat Hanrahan

What is BSSRDF?

• Bidirectional surface scattering reflectance distribution function

• In other words… An equation that determines how incident light reflects and scatters from a surface

• Also, simulates how light reflects off of and throughout a surface

Example: Skin

BRDF

• Bidirectional reflectance distribution function

• Simplification of BSSRDF

• Assumes that light entering a material leaves it at the same point

• Usually tries to approximate surface scattering in some way

BSSRDF v. BRDF

• BSSRDF allows simulation of light transport

• Light can enter a material at one point and be reflected at another point.

• BSSRDF Translucence, Color Bleeding

• BRDF Opague, Hard-looking…

• But… BSSRDF is EXPENSIVE

BSSRDF v. BRDF

BRDF BSSRDF

BRDF BSSRDF

Example

The Theory

• Outgoing radiance at point x0 is computed by integrating incident radiance at points xi over the surrounding area and incoming directions wi.

Hendrik Wann Jensen et al

• Basic Idea: Break into two parts

• Diffuse = the radiance at a given point due to light transport within the media, via an approximation of the scatting

• Single Scattering = the first order scattering from a surface… BRDF reflection + light refracted through the material

Diffuse vs. Single Scatter

The Diffusion Approximation

• In highly scattering media (like milk), light scatters many times (often several hundred)

• Causes a lot more calculations, more expensive (if you use full BSSRDF)

Diff. Approx. (cont.) = Sd

• It is observed that in such materials the scattering becomes isotropic (in all directions) even with a highly focused light distribution.

• So the following two-term approximation is used:

radiant fluence

vector irradiance

Single Scattering Term = S(1)

• The light which refracts directly through or reflects off of the material

• Directional component of incident light

• Jensen (et al) extend a BRDF model (Hanrahan and Krueger) to achieve this scatter

Putting the two together…

• So Jensen’s model of BSSRDF becomes:

• Or:

• BSSRDF = Diffuse Approximation + Single Scatter Term

Light propagation

• a = Absorption Coefficient

• s = Scattering Coefficient

• t = Extinction Coefficient = a + s

• These are used in the volume rendering equation, which describes how light moves through a medium

Getting the Coefficients

Got Milk?

Marble bust

1.3 Million Triangles

BRDF: 2 minutes

BSSRDF: <5 minutes

Monte Carlo: 1250 minutes

Stanford Bunny

Future Plans of Hendrik Wann Jensen

• In an interview of Jensen by CGarchitect.com:“I would like to combine the BSSRDF with photon mapping, and also work on making these algorithms generally available and easy to use for complex models.”

FinalRender

• First Render Engine to support BSSRDF

• More Info: http://trinity3d.comhttp://trinity3d.com/productinfo/FinalRender/finalrender.shtml